Let's Wait a While

I've often confused the difference between "awhile" and "a while" so I decided to do some research and here's what Brian's Common English Errors Website had to say about this:

When “awhile” is spelled as a single word, it is an adverb meaning “for a time."

So you would say:
"My Prince Charming was bored with me awhile."

But when “while” is the object of a prepositional phrase the “while” must be separated from the “a.”

Then you would say:
"Did you have Prince Charming's CD for a while or only after you broke up?"

The site also makes not that if the preposition “for” were lacking in this sentence, “awhile” could be used in this way:

"Did you have Prince Charming's CD awhile?"